Table 8: The 9-dimensional nilsoliton metric Lie algebra candidates of nullity 3.

Lie bracket Index Nullity

69 (0, 0, 1.12, 1.13, 1.14 + 1.23, 0, 1.16 + 1.25 + 1.34, 1.17, 1.18 + 1.27 + 1.45) 6 3
70 (0, 0, 1.12, 1.13, 1.14 + 1.23, 0, 1.16 + 1.25 + 1.34, 1.17, 1.18 + 1.27 + 1.36) 6 3
71 (0, 0, 1.12, 1.13, 1.14 + 1.23, 0, 1.16 + 1.25 + 1.34, 1.17 + 1.35, 1.18 + 1.27) 6 3
72 (0, 0, 1.12, 1.13, 1.14 + 1.23, 0, 1.16 + 1.25 + 1.34, 1.17 + 1.26, 1.18 + 1.45) 6 3
73 (0, 0, 1.12, 1.13, 1.14 + 1.23, 0, 1.16 + 1.25 + 1.34, 1.17 + 1.26 + 1.35, 1.18) 6 3
74 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.25 + 1.34, 1.26, 1.18 + 1.27 + 1.36 + 1.45) 6 3
75 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.25 + 1.34, 1.26 + 1.35, 1.18 + 1.27 + 1.45) 6 3
76 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.25 + 1.34, 1.26 + 1.35, 1.18 + 1.27 + 1.36) 6 3
77 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.25 + 1.34, 1.17, 1.18 + 1.27 + 1.36 + 1.45) 6 3
78 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.25 + 1.34, 1.17 + 1.35, 1.18 + 1.27 + 1.36) 6 3
79 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.26, 1.27 + 1.36 + 1.45) 7 3
80 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.26 + 1.35, 1.27 + 1.45) 7 3
81 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.26 + 1.35, 1.27 + 1.36) 7 3
82 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.35, 1.18 + 1.27 + 1.45) 7 3
83 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.35, 1.18 + 1.27 + 1.36) 7 3
84 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.26, 1.18 + 1.27 + 1.45) 7 3
85 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.26, 1.18 + 1.27 + 1.36) 7 3
86 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.26 + 1.35, 1.18 + 1.27) 7 3
87 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.17, 1.27 + 1.36 + 1.45) 6 3
88 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.17 + 1.35, 1.27 + 1.45) 6 3
89 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.17 + 1.35, 1.27 + 1.36) 6 3
90 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.17, 1.18 + 1.27 + 1.45) 7 3
91 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.17, 1.18 + 1.27 + 1.36) 7 3
92 (0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.17 + 1.35, 1.18 + 1.27) 7 3
93 (0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.34, 1.17 + 1.35, 1.18) 7 3
94 (0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.34, 1.17 + 1.26, 1.18) 7 3
95 (0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25, 1.17, 1.18 + 1.45) 7 3
96 (0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25, 1.17, 1.18 + 1.36) 7 3
97 (0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25, 1.17 + 1.35, 1.18) 7 3
98 (0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17, 1.18) 7 3